The talented midfielder is expected to play a big role for the Gers next season.
The 19-year-old arrived earlier this summer on a free transfer after his contract with Liverpool expired, but he has yet to link up with the Gers squad due to his participation at the under-19 European Championship in Germany.
“We can see the pedigree, the talent and attitude of the boy,” said Warburton.
“Everyone has benefited from a move like his. He had a very good game for England’s Under-19 side in midweek against France. He was always looking to get on the ball…I was delighted with what I saw.
“Hopefully he can carry that on in the tournament. He’ll come back in a good state of fitness and should fit in seamlessly…He’ll be eager to play for us when he gets back,” he added.
Rangers’ capture of the former Liverpool man is regarded as a major coup, with Rossiter viewed as one of the country’s brightest young talents.
The Gers exploited a regulatory loophole which allowed the club to avoid having to pay a transfer fee set by a tribunal – a tactic which Warburton recently defended – and big things are expected of the energetic midfielder at Ibrox.
Competition for places at the heart of Rangers’ midfield will be intense next season, with the likes of Joey Barton, Nico Kranjcar and Rossiter adding to the current crop but it will ensure that Warburton can keep things fresh in one of the most important areas of the pitch.
Rangers face the difficult task of halting Celtic’s march for a sixth consecutive title and will need all the squad depth they can muster if they are to be successful.